# Direct-product-closed subgroup property

From Groupprops

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property

View a complete list of subgroup metaproperties

View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Definition with symbols

A subgroup property is said to be **direct-product-closed** if whenever satisfies , and satisfies , then satisfies as a subgroup of .

## Relation with other metaproperties

### Stronger metaproperties

- Intersection-closed subgroup property that also satisfies inverse image condition

### Weaker metaproperties

### Related metaproperties

- Subgroup properties satisfying image condition
- Subgroup properties satisfying inverse image condition
- Subgroup properties satisfying transfer condition
- Subgroup properties satisfying intermediate subgroup condition